Ohm's Law Formula

Q: What is the Ohm's Law formula?

The fundamental relationship stating that the voltage ($V$) across an ohmic conductor equals the current ($I$) flowing through it multiplied by its resistance ($R$).

Q: What do the symbols mean in the Ohm's Law formula?

$V$ is the potential difference in volts (V), $I$ is the current in amperes (A), $R$ is the resistance in ohms ($\Omega$), $\vec{J}$ is the current density in A/m², and $\sigma$ is the electrical conductivity in S/m.

The Formula

V = IR or equivalently I = \frac{V}{R} or R = \frac{V}{I}

When to use: More push (voltage) means more flow (current). More resistance means less flow for the same push.

Quick Example

A 12 V battery connected to a 4 \Omega resistor: I = \frac{12}{4} = 3 A.

Notation

V is the potential difference in volts (V), I is the current in amperes (A), R is the resistance in ohms (\Omega), \vec{J} is the current density in A/m², and \sigma is the electrical conductivity in S/m.

What This Formula Means

The fundamental relationship stating that the voltage (V) across an ohmic conductor equals the current (I) flowing through it multiplied by its resistance (R).

More push (voltage) means more flow (current). More resistance means less flow for the same push.

Formal View

Ohm's law for a linear (ohmic) conductor is V = IR, where R is constant. In differential form, \vec{J} = \sigma \vec{E}, where \vec{J} is current density and \sigma = 1/\rho is the conductivity. Ohm's law is an empirical relation, not a fundamental law of physics.

Worked Examples

Example 1

easy

A 12 \text{ V} battery is connected to a 4 \text{ } \Omega resistor. What current flows?

Solution

1
Apply Ohm's law: I = \frac{V}{R}.
2
Substitute the values: I = \frac{12}{4}.
3
I = 3 \text{ A}

Answer

I = 3 \text{ A}

Ohm's law (V = IR) is the fundamental relationship in circuit analysis. It connects voltage, current, and resistance in a simple linear relationship.

Example 2

medium

A heater draws 5 \text{ A} from a 240 \text{ V} supply. What is its resistance, and how much power does it consume?

Common Mistakes

Applying Ohm's law to the entire circuit when resistors are in parallel — Ohm's law relates the voltage across a single component to the current through that component; use equivalent resistance for the full circuit.
Thinking Ohm's law applies to all materials — it only holds for ohmic conductors (like metals at constant temperature); diodes, LEDs, and filament bulbs are non-ohmic.
Using milliamps or kilohms without converting — all values must be in base units (amps, volts, ohms) before substituting into V = IR.

Common Mistakes Guide

If this formula feels simple in isolation but keeps breaking during real problems, review the most common errors before you practice again.

Electric Current Mistakes

Why This Formula Matters

Ohm's law is the single most-used equation in circuit analysis and electrical engineering. It is essential for calculating current draw, sizing wires, designing circuits, troubleshooting faults, and ensuring electrical safety in homes and industry.

Frequently Asked Questions

What is the Ohm's Law formula?

The fundamental relationship stating that the voltage (V) across an ohmic conductor equals the current (I) flowing through it multiplied by its resistance (R).